Leveraged and inverse ETFs

The objective is written for one day 

A leveraged fund states in its own documentation that it seeks a stated multiple of the return of an index for a single day, measured close to close. An inverse fund states that it seeks the opposite of that index's return, again for a single day. The word that carries the weight in both sentences is daily. The objective is not written for a week, a month or a year, and the fund's managers do not undertake to deliver the multiple over any period longer than one session.

Within that single day the arithmetic is symmetric and it runs in both directions. A fall in the index produces a loss on the fund of the multiplied size, and losses on such a fund are therefore larger than losses on the ordinary fund tracking the same index by exactly that factor. A rise produces a gain calculated the same way. The structure does not favour either direction, and nothing about it reduces the size of an adverse move.

How the exposure is obtained 

These funds hold derivatives rather than a multiplied quantity of shares. The usual construction is a combination of total return swaps with bank counterparties, index futures and, in some cases, a holding of the index constituents alongside them, with cash held as collateral. The swap counterparty pays the fund the index return on an agreed notional amount and the fund pays a financing rate in exchange, which is one of the reasons a fund of this type costs more to run than a plain tracking fund.

Because the objective is defined per day, the notional exposure has to be reset at every close so that the following day starts at the stated multiple of the fund's own new net assets. That reset is a real trade. After a day on which the index rose, a leveraged fund has to add exposure; after a day on which it fell, it has to reduce exposure. The reset therefore moves in the same direction as the market that day, which is why concentrated flows from these funds are discussed as a possible contributor to late session movement in the instruments they reference.

The reset makes the longer result path dependent 

Holding a fund of this type for more than one day compounds a sequence of daily results rather than applying the multiple to the period as a whole. Compounding is not linear, so the outcome depends on the order and the size of the daily moves and not only on where the index finished. The clearest illustration is a case in which the index ends exactly where it started.

The result is not a tracking failure. The fund did exactly what its documentation said it would do on each of the two days. The shortfall comes from compounding a larger daily percentage against a base that has itself changed, and it appears whenever daily moves alternate in direction. The effect grows with the size of the daily moves, which is why it is commonly discussed in terms of volatility, and it accumulates the longer such a position is held through a range bound market.

In a market that moves in one direction for many days without interruption, compounding runs the other way and the period result can exceed the stated multiple of the index's period move. That case is stated here for completeness rather than as an expectation: which of the two regimes a period turns out to have been is known only afterwards, and the same mechanism produces a compounded loss that exceeds the multiple when the sustained move runs against the position.

Inverse funds carry a further asymmetry 

A fund seeking the opposite of an index's daily return holds short exposure through swaps or futures, and it resets that exposure daily in the same way. Two features distinguish it from a leveraged long fund. First, the arithmetic of a short exposure is asymmetric at the level of a single move: a market that falls can fall by no more than its entire value, while a market that rises has no arithmetic ceiling, so an adverse move against short exposure is unbounded in a way a favourable one is not. Second, holding short exposure has its own running cost, since the counterparty prices the borrow of the underlying into the swap, and that cost is higher for instruments that are difficult or expensive to borrow.

Inverse funds are also the clearest case of the daily objective being misread. Over a long horizon most broad equity indices have risen, so a fund resetting short exposure against one has compounded a sequence of adverse days as well as favourable ones, and its long horizon record reflects the compounding rather than the simple inverse of the index's total move.

What these funds cost to run 

Three cost lines sit inside a fund of this type and none of them is invoiced to a holder. The management fee accrues daily inside the portfolio, as in any fund, and it is typically higher than a plain index fund's because the strategy is more complex to administer. The financing embedded in the swaps and futures accrues continuously, because exposure larger than the fund's assets has to be funded by somebody. The daily reset generates trading costs, which rise with the volatility of the index being referenced. All three reduce net asset value, and therefore the price the fund's shares trade around, before any market move is considered.

What the fund's own documents say 

Issuers of these funds state the daily objective and its consequences prominently and in their own words. The prospectus of a fund of this type conventionally records that the fund seeks its objective for a single day, that its results over longer periods will differ from the multiple of the index's return over that period, and that the difference is likely to be more pronounced when the index is volatile. Several regulators require additional disclosure or a suitability assessment before such products are distributed to retail investors, and some have restricted their distribution altogether. Those statements come from the issuer and the regulator, and they are the primary source on how the instrument is meant to be understood.

As the underlying of a contract for difference 

Where a contract for difference is written on a fund of this kind, the contract references the fund's listed price and settles the change in it in cash. Two separate mechanisms are then present at once. The fund resets its own exposure daily inside the portfolio, which is what produces the compounding described above. The contract, separately, is funded by margin, so its profit and loss are calculated on the full contract value rather than on the money posted against it. The two are independent of each other, and the loss produced by an adverse move is calculated through both.